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Introduction to Biomechanics and Vector Resolution

Introduction to Biomechanics and Vector Resolution. Applied Kinesiology 420:151. Agenda. Introduction to biomechanics Units of measurement Scalar and vector analysis Combination and resolution Graphic and trigonometric methods. Introduction to Biomechanics. Biomechanics.

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Introduction to Biomechanics and Vector Resolution

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  1. Introduction to Biomechanics and Vector Resolution Applied Kinesiology 420:151

  2. Agenda • Introduction to biomechanics • Units of measurement • Scalar and vector analysis • Combination and resolution • Graphic and trigonometric methods

  3. Introduction to Biomechanics Biomechanics The study of biological motion Statics Dynamics The study of forces on the body in equilibrium The study of forces on the body subject to unbalance Kinetics and Kinematics Kinetics and Kinematics Kinetics: The study of the effect of forces on the body Kinematics: The geometry of motion in reference to time and displacement Linear vs. Angular Linear vs. Angular Linear: A point moving along a line Angular: A line moving around a point

  4. Agenda • Introduction to biomechanics • Units of measurement • Scalar and vector analysis • Combination and resolution • Graphic and trigonometric methods

  5. Units of Measurement • Systeme Internationale (SI) • Base units • Derived units • Others

  6. SI Base Units • Length: SI unit  meter (m) • Time: SI unit  second (s) • Mass: SI unit  kilogram (kg) • Distinction: Mass (kg) vs. weight (lbs.) • Mass: Quantity of matter • Weight: Effect of gravity on matter • Mass and weight on earth vs. moon?

  7. SI Derived Units • Displacement: A change in position • SI unit  m • Displacement vs. distance? • Velocity: The rate of displacement • SI unit  m/s • Velocity vs. speed? • Acceleration: The rate of change in velocity • SI unit  m/s/s or m/s2

  8. SI Derived Units • Force: The product of mass and acceleration • SI Unit  Newton (N)  The force that is able to accelerate 1 kg by 1 m/s2 • How many N of force does a 100 kg person exert while standing? • Moment: The rotary action of a force • Moment = Fd • SI Unit  N*m  When 1 N of force is applied at a distance of 1 m away from the axis of rotation

  9. SI Derived Units Deadlift Example • Work: The product of force and distance • SI Unit  Joule (J)  When 1 N of force moves through 1 m • Note: 1 J = 1 N*m • Energy: The capacity to do work • SI Unit  J • Note: 1 J = ~ 4 kcal • Power: The rate of doing work (work/time) • SI Unit  Watt (W)  When 1 J (or N*m) is performed in 1 s • Note: Also calculated as F*V

  10. Other Units • Area: The superficial contents or surface within any given lines • 2D in nature • SI Unit  m2 • Volume: The amount of space occupied by a 3D structure • SI Unit  m3 or liter (l) • Note: 1 l = 1 m3

  11. Agenda • Introduction to biomechanics • Units of measurement • Scalar and vector analysis • Combination and resolution • Graphic and trigonometric methods

  12. Scalar and Vector Analysis • Scalar defined: Single quantities of magnitude  no description of direction • A speed of 10 m/s • A mass of 10 kg • A distance of 10 m • Vector defined: Double quantities of magnitude and direction • A velocity of 10 m/s in forward direction • A vertical force of 10 N • A displacement of 10 m in easterly direction

  13. Scalar and Vector Representation • Scalars are represented as values that represent the magnitude of the quantity • Vectors are represented as arrows that represent: • The direction of the vector quantity (where is the arrow pointing?) • The magnitude of the vector (how long is the arrow?)

  14. Figure 10.1, Hamilton

  15. Combination of Vectors • Vectors can be combined which results in a new vector called the resultant. • We can combine vectors three ways: • Addition • Subtraction • Multiplication

  16. Vector Combination: Addition • Tip to tail method • The resultant vector is represented by the distance between the tail of first vector and the tip of the second + = Vector 1 Vector 2 Resultant

  17. Vector Combination: Subtraction • Tip to tail method • Resultant = Vector 1 – Vector 2 or . . . • Resultant = Vector 1 + (- Vector 2) • Flip direction of negative vector + = Vector 1 Vector 2 Resultant

  18. Vector Combination: Multiplication • Tip to tail method • Only affects magnitude • Same as adding vectors with same direction X 3 =

  19. Vector Resolution • Resolution: The breakdown of vectors into two sub-vectors acting at right angles to one another

  20. Resultant velocity of shot at take off is a function of the horizontal velocity (B) and the vertical velocity (A)

  21. Location of Vectors in Space • Frame of reference: • Reality = 3D  2D for simplicity • Two types: • Rectangular coordinate system • Polar coordinate system

  22. Rectangular Coordinate System Y (-,+) (+,+) X (+,-) (-,-) The vector starts at (0,0) and ends at (x,y) Example: Vector (4,3)

  23. Polar Coordinate System Figure 10.5, Hamilton Coordinates are (r,q) where r = length of resultant and q= angle

  24. Figure 10.6, Hamilton

  25. Graphic Resolution of Vectors • Tools: Graph paper, pencil, protractor • Step 1: Select a linear conversion factor • Example: 1 cm = 1 m/s, 1 N or 1 m etc. • Step 2: Draw in force vector based on frame of reference • Step 3: Resolve vector by drawing in vertical and horizontal subcomponents • Step 4: Carefully measure and convert length of vectors to quantity

  26. Conversion factor: 1 cm = 1 m Combination? Tip to tail method! With the protractor and ruler, measure measure a vector that is 5.5 cm long with a take-off angle of 18 degrees at (0,0) Horizontal velocity = 5.2 m/s Vertical velocity = 1.7 m/s 5.5 cm 1.7 cm 18 deg 5.2 cm Assume a person performs a long jump with a take-off velocity of 5.5 m/s and a take-off angle of 18 degrees. What are the horizontal and vertical velocities at take-off?

  27. Trigonometric Resolution of Vectors • Advantages: • Does not require precise drawing • Time efficiency and accuracy

  28. Trigonometry Terminology • Trigonometry: Measure of triangles • Right triangle: A triangle that contains an internal angle of 90 degrees (sum = 180 degrees) • Acute angle: An angle < 90 deg • Obtuse angle: An angle > 90 deg

  29. Trigonometry Terminology • Hypotenuse: The side of the triangle opposite of the right angle (longest side) • Opposite leg: The side not connected to angle in question • Adjacent leg: The side connected to angle in question (but not hypotenuse) H O Angle in Q A

  30. Trigonometry Functions • Sine: Sine of an angle = O/H • Cosine: Cosine of an angle = A/H • Tangent: Tangent of an angle = O/A Soh Cah Toa Online Scientific Calculator  http://www.creativearts.com/scientificcalculator

  31. Trigonometric Resolution of Vectors Figure 10.11, Hamilton

  32. Trigonometric Resolution of Vectors Pythagorean Theorum Figure 10.12, Hamilton

  33. Trigonometric Combination of Vectors • Step 1: Resolve all vertical and horizontal components of all vectors • Step 2: Sum the vertical components together for a new vertical component • Step 3: Sum the horizontal components for a new horizontal component • Step 4: Generate new vector based on new vertical and horizontal components

  34. Figure 10.13, Hamilton

  35. Figure 10.13, Hamilton

  36. Trigonometric Combination of Several Vectors Figure 10.14, Hamilton

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